Guessing, but when you hit the throttle hard, batt voltage is dropping below what the failsafe is set at. Either set failsafe lower (not familar with your setup so I don't know if thats possible) or disable it and retest. If you have to disable it to make it run when throttle is mashed, at least you know its your batts and not the radio. Maybe running a rx pac to get the onboard elec load of the main batts could help - depends on how much below the cutoff batts are dropping.

Other solution - better batts or lipo.